99=20t-t^2

Solution for 99=20t-t^2 equation:

Simplifying
99 = 20t + -1t2

Solving
99 = 20t + -1t2

Solving for variable 't'.

Reorder the terms:
99 + -20t + t2 = 20t + -20t + -1t2 + t2

Combine like terms: 20t + -20t = 0
99 + -20t + t2 = 0 + -1t2 + t2
99 + -20t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
99 + -20t + t2 = 0

Factor a trinomial.
(9 + -1t)(11 + -1t) = 0

Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Subproblem 2
Set the factor '(11 + -1t)' equal to zero and attempt to solve:

Simplifying
11 + -1t = 0

Solving
11 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -1t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1t = 0 + -11
-1t = 0 + -11

Combine like terms: 0 + -11 = -11
-1t = -11

Divide each side by '-1'.
t = 11

Simplifying
t = 11
Solution
t = {9, 11}